High-Quality Single Crystalline Sc0.37Al0.63N Thin Films Enabled by Precise Tuning of III/N Atomic Flux Ratio during Molecular Beam Epitaxy

We attained wurtzite ScxAl1−xN (0.16 ≤ x ≤ 0.37) thin films by varying the Sc and Al fluxes at a fixed active nitrogen flux during plasma-assisted molecular beam epitaxy. Atomic fluxes of Sc and Al sources via measured Sc percentage in as-grown ScxAl1−xN thin films were derived as the feedback for precise determination of the ScxAl1−xN growth diagram. We identified an optimal III/N atomic flux ratio of 0.78 for smooth Sc0.18Al0.82N thin films. Further increasing the III/N ratio led to phase separation under N-rich conditions, validated by the observation of high-Sc-content hillocks with energy-dispersive X-ray spectroscopy mapping. At the fixed III/N ratio of 0.78, we found that phase separation with high-Al-content hillocks occurs for x > 0.37, which is substantially lower than the thermodynamically dictated threshold Sc content of ~0.55 in wurtzite ScxAl1−xN. We postulate that these wurtzite-phase purity degradation scenarios are correlated with adatom diffusion and the competitive incorporation process of Sc and Al. Therefore, the ScxAl1−xN growth window is severely restricted by the adatom kinetics. We obtained single crystalline Sc0.37Al0.63N thin films with X-ray diffraction (002)/(102) ω rocking curve full-width at half-maximums of 2156 arcsec and 209 arcsec and surface roughness of 1.70 nm. Piezoelectric force microscopy probing of the Sc0.37Al0.63N epilayer validates unambiguous polarization flipping by 180°.


Introduction
Recently, the development of epitaxial Sc-alloyed wurtzite III-nitrides has attracted significant research attention due to the enhancement of the c-axis piezoelectric response and spontaneous polarization [1].By substituting Al sites in the wurtzite AlN lattice with Sc (Sc x Al 1−x N), the coefficient of piezoelectric modulus d 33 could be enhanced by a factor of 4-5 at a Sc content of 0.43 [2,3].The increase in d 33 relative to AlN translates into stronger electromechanical coupling in film bulk acoustic resonators (FBARs) and therefore broader bandwidth [4].As the Sc content increases in the AlN matrix, the transition from wurtzite lattice towards layered hexagonal lattice is characterized by an increasing internal parameter from 0.38 to 0.50 [5] and boosted spontaneous polarization (2× for x = 0.40) [6], enabling versatile polarization engineering in III-nitride optoelectronic heterostructures.In 2019, S. Fichtner et al. demonstrated ferroelectric polarization switching with x ≥ 0.27 [7].The unprecedently high paraelectric transition temperature of Sc x Al 1−x N (>600 • C) enables stable operation under harsh environments [8].Potential ferroelectric memory applications call for a lower coercive field in order to reduce power consumption [9], which demands higher Sc content close to the boundary of wurtzite-phase purity.Therefore, increasing the Sc composition in wurtzite Sc x Al 1−x N alloys would have a drastic impact on the sub-6GHz resonant filter and high-temperature ferroelectric memory applications.
To date, multiple research groups have demonstrated single crystalline Sc x Al 1−x N/GaN heterostructures grown via plasma-assisted molecular beam epitaxy (PA-MBE) with an Sc content of x ~0.18 targeting high-frequency power electronic applications [10][11][12][13].The empirical MBE growth window has been investigated based on the beam equivalent pressures (BEPs) of Sc and Al sources, and "N-rich" conditions, i.e., (Sc BEP + Al BEP ) < N BEP (N BEP is an equivalent flux derived from AlN growth), were selected for Sc x Al 1−x N alloy growth [11].To maintain sufficient Al and Sc adatom diffusion for single crystalline growth, the elevated growth temperature (T sub = 600-900 • C) in PA-MBE has been correlated with the degradation of wurtzite-phase purity in high-Sc-content Sc x Al 1−x N (x > 0.30) thin films [14]; whereas the effect of precisely tuning Al, Sc, and active N atomic fluxes on Sc x Al 1−x N phase separation remains elusive.Traditional high-Sc-content Sc x Al 1−x N (x > 0.30) were deposited via magnetron sputtering at reduced temperatures (~400 • C), which exhibited fiber-textured characteristics, i.e., hexagonal columns aligned along the c-axis and quasi-random in-plane crystalline orientation [15][16][17][18].Even though the pseudosixfold symmetry of in-plane orientation has been observed while molybdenum or tungsten buffer layers were used [9], sputtered Sc x Al 1−x N (x > 0.20) layers generally require sufficient thickness (~1 µm) in order to achieve an X-ray diffraction (XRD) (002) ω rocking curve full-width at half-maximum (FWHM) of ~1• [16], and "undesired crystallites" in sputtered Sc x Al 1−x N (x > 0.20) have a detrimental effect on the electromechanical coupling coefficient [19].However, scatter loss due to grain boundaries in polycrystalline thin films reduces the resonance quality factor; and meanwhile, the further upscaling of the resonant frequency demands the downscaling of the film thickness [17].Next-generation ferroelectric memory arrays also demand ultra-thin high-Sc-content Sc x Al 1−x N (<200 nm, x > 0.30) with single crystallinity to reduce power consumption and to balance the requirements of miniaturization and reliability.To our knowledge, the most representative high-Sc-content Sc x Al 1−x N (x > 0.30) thin films were reported by M. Hardy et al., with XRD (002) ω rocking curve FWHMs of 1840 arcsec for x = 0.32 [14] and 3190 arcsec for x = 0.39 [20], respectively.It is critical to elucidate the MBE growth diagram of wurtzite Sc x Al 1−x N alloys at such high Sc composition further and to improve the crystalline quality.
In this work, we have investigated the PA-MBE growth window of Sc x Al 1−x N thin films on the basis of the precise determination of Sc, Al, and active N atomic fluxes.Two distinctive types of phase separation were identified: (1) at a fixed Sc-to-Al atomic flux ratio for x = 0.18, undesirable Sc-agglomerated hillocks occur when the oversupply of active N is less than 15%; i.e., III/N ratio > 0.85; and (2) at a fixed III/N ratio of 0.78 for high Sc content (x > 0.30), Al-agglomerated hillocks start to emerge in the Sc x Al 1−x N thin film when the Sc/Al atomic flux ratio is over 60%; i.e., x > 0.37.Both phase separation scenarios provide novel insight to the growth diagram of Sc x Al 1−x N alloys, validating that the thermodynamic requirements of (i) N-rich synthesis conditions and (ii) Sc content x < 0.55 for stable wurtzite Sc x Al 1−x N are inadequate at a growth temperature of 680 • C (pyrometer).The kinetic growth regime of PA-MBE, particularly the adatom surface diffusion and incorporation processes, could fundamentally affect the wurtzite-phase purity of Sc x Al 1−x N.With this updated knowledge, we attained 100 nm thick single crystalline Sc 0.37 Al 0.63 N thin films with XRD (002) and (102) ω rocking curve FWHMs of 2156 arcsec and 209 arcsec and a mean square surface roughness (RMS) of 1.70 nm.Polarization switching by 180 • is validated by applying a bias of ±15 V under piezoelectric force microscopy (PFM), promising potential applications in ferroelectrics.Our work provides guidance for the PA-MBE growth of high-Sc-content Sc x Al 1−x N thin films and paves the way towards novel applications for the strongly polarized wide-bandgap material.

Experimental Details
Unintentionally doped Sc x Al 1−x N films were grown on 2-inch Si(111) substrates and on GaN on sapphire (GaN/sapphire) templates using an in-house customized PA-MBE system (Fermion Instruments Corp., Ltd., Nanjing, P.R. China).A type-C thermocouple placed at 3 mm in proximity to the backside of the template/substrate was used for T sub control; and meanwhile, a pyrometer was installed to monitor the temperature of template/substrate surface.To keep the growth temperatures of Sc x Al 1−x N on Si(111) substrates and on GaN/sapphire templates comparable, we used the pyrometer to monitor the surface temperatures of both types of substrates, and the thermocouple temperature was adjusted to ensure a pyrometer temperature of 680 • C before the growth of Sc x Al 1−x N, while the discrepancy in thermocouple temperatures of Si(111) substrates and of GaN/sapphire templates reached 30 • C. Once the growth started, we kept the thermocouple temperature constant even though the pyrometer temperature generally varied by 5-20 • C during Sc x Al 1−x N growth.Standard SUMO cells were equipped with a cold-lip pyrolytic boron nitride (PBN) crucible for high-purity Al (6N5) ingots and two hot-lip PBN crucibles for Sc (4N) and Ga (7N5), respectively.The Al cell was heated to 1050-1100 • C to provide a beam equivalent flux (BEP) of 2.0 × 10 −8 -5.0 × 10 −8 Torr, the Sc cell was heated to 1150-1250 • C to provide a BEP of 5.0 × 10 −9 -3.0 × 10 −8 Torr, and the Ga cell was heated to 950-1000 • C to provide a BEP of 2.0 × 10 −7 -5.0 × 10 −7 Torr.A 13.56 MHz inductively coupled N 2 plasma cell was used with a mass flow controller to tune high-purity N 2 (6N) gas at 0.35 standard centimeters per minute (sccm) and with a radio-frequency impedance matching box to sustain a plasma power of 350 W. The atomic flux of active nitrogen was calculated using an AlN growth rate at 180 nm/h grown under metal-rich conditions.The MBE chamber was equipped with in situ reflection high-energy electron diffraction (RHEED, Dr. Glasser electron devices GmbH, Ulm, Germany).
Two types of substrates, Si(111) substrates and commercial 4 µm thick GaN/sapphire templates grown via metal organic vapor-phase epitaxy (MOCVD), were utilized for Sc x Al 1−x N growth.Hoglund et al. reported the effect of the substrate on the achievable Sc composition of pure wurtzite phase [21,22], demonstrating correlation between strain energy and phase stability [23].K. Yazawa et al. and V. Gund et al. reported that inplane tensile film stress can effectively push the phase separation boundary of wurtzite Sc x Al 1−x N towards higher Sc percentage [9,24].Herein, we focus on the effect of III/N on Sc x Al 1−x N film growth kinetics, while the proper choice of substrate for different Sc compositions enables a similar strain state during Sc x Al 1−x N nucleation.
Samples C1-C4 with Sc content x = 0.18 were grown on Si(111) substrates using a 50 nm thick AlN buffer layer to mimic the compressive strain state of Sc x Al 1−x N (x > 0.18) grown on GaN/sapphire templates.The Si(111) substrate was outgassed at 800 • C for 1 h in the preparation chamber, and after transfer to the growth position, it was baked at 900 • C for 30 min prior to growth.Samples C5-C9 with Sc content x varying from 0.16 to 0.39 were grown on GaN/sapphire using a 100 nm thick GaN buffer layer.The backsides of the GaN/sapphire templates were sputter-coated with 2 µm thick titanium to enhance heat absorption.The GaN/sapphire templates were cleaned in ultrasonic baths of acetone and isopropanol, rinsed with deionized water, and blown dry in dry N 2 prior to their loading into the MBE loadlock.Subsequently, the templates were outgassed at 450 • C for 2 h in the preparation chamber and at 600 • C for 30 min in the growth chamber prior to growth.
Surface morphology of as-grown samples was characterized using a Bruker ICON atomic force microscope (AFM, Bruker Corp., Billerica, United States) in tapping mode and a Hitachi S4800 scanning electron microscope (SEM, Hitachi High-Tech Corp., Hitachinaka, Japan).Sample thickness was measured via cross-sectional SEM.The Sc content x was determined via two independent approaches: X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS).XRD 2θ-ω scans and ω rocking curve scans were performed on a PANalytical X'pert3 MRD high-resolution X-ray diffractometer equipped with Cu-K α radiation (λ = 1.54056Å at 40 kV and 45 mA), a Ge symmetric four-bounce monochromator, and a scintillator detector (Malvern Panalytical.Co., Malvern, UK).A Thermo Fisher ESCALAB QXi XPS system with an Al-K α X-ray source (1486.6 eV) was used for chemical composition analysis (ThermoFisher Scientific, Waltham, MA, USA).Energy dispersive X-ray (EDX) spectroscopy was acquired using a FEI Nova Nano SEM 450 system equipped with an Octane Super EDX detector (AMETEK Inc., Berwyn, IL, USA).PFM measurements were conducted using a commercial atomic force microscope (Asylum Research MFP-3D, Oxford Instruments, Santa Barbara, CA, USA).The amplitude and phase patterns were mapped with a writing voltage of ±15 V, and the GaN buffer layer was grounded.An AC voltage with an amplitude of 600 mV and a contact resonance frequency of approximately 30 kHz was applied to the tip during PFM measurement.

Results and Discussion
3.1.Effect of III/N Atomic Flux Ratio on Sc 0.18 Al 0.82 N Growth The thermodynamic preference of intermetallic Al x Sc y phases dictates N-rich growth conditions for Sc x Al 1−x N [12,13].Z. Engel et al. demonstrated that under a high nominal III/N ratio of ~1.5, catalytic cracking of N 2 by accumulated metallic Sc effectively reduces III/N atomic ratio at the growth front [25].This effect is largely suppressed under N-rich conditions.In previous studies on the MBE growth of Sc x Al 1−x N films, the optimal III/N ratio values were scattered in a range of 0.50-0.85;they were determined by the sum of Sc and Al BEPs over the active nitrogen flux derived from the Al-rich growth of AlN [14,26,27].However, depending upon the geometrical configuration of the MBE reactor and the responsivity of the flux monitor, the normalization factor between the true atomic flux and the nominal BEP could be radically different for Sc and Al sources.As such, it is necessary to calibrate the true atomic flux of Sc and Al, which can be derived from the film thickness and Sc composition of as-grown Sc x Al 1−x N. Specifically, the normalization factor for the Sc source reaches 65.0% that of the Al source in our MBE chamber, whereas the normalization factor for the Sc source was calibrated to be 97.7% that of the Al source, as reported by K. Frei et al. [12].Herein, we utilized the atomic flux ratio of III/N as a universal gauge to investigate MBE growth diagram.
Our comparison of Sc 0.18 Al 0.82 N films grown under various III/N atomic flux ratios of 0.69-1.12demonstrates that streaky RHEED patterns and a smooth surface can be achieved at an optimal flux ratio at 0.78, and that a further increase in III/N ratio, even within the N-rich regime, leads to spotty RHEED patterns and densely packed hillocks across the surface.At III/N = 0.69 (sample C1), the planar-view SEM in Figure 1a shows the incomplete coalescence of individual crystallites, resembling columnar microstructures with a lateral grain size of 100-300 nm.The corresponding RHEED patterns exhibit streaks and arcs, indicating in-plane angular twisting of grains [20].By increasing the III/N ratio to 0.78 (sample C2), RHEED patterns in Figure 1b exhibit sharper streaks without any arcs.The significantly improved film smoothness implies enhanced adatom mobility, promoting the growth mode from 3D to 2D.At even higher III/N = 0.89 (sample C3), we observed densely packed hillocks of ~300 nm in diameter across the surface, while the RHEED patterns became spotty with emerging ring-like characteristics.Further increasing the III/N ratio to the metal-rich regime (sample C4) led to similar but slightly dimmer RHEED patterns; meanwhile, the surface hillocks evolved towards a coalesced terrace, exhibiting elongated hexagonal features.No Sc dendrites or intermetallic droplets can be observed in Figure 1c,d [12,25].
We conducted EDX scans to investigate elemental distribution of Al and Sc across the films.EDX spectra taken under accelerating voltages of 5 keV and 10 keV were shown in Figure S1 (Supplementary Material S1).The electron energy of 5 keV in the primary beam is slightly higher than the critical excitation energy of the K shell in Sc (4.492 keV).An overvoltage ratio of >2 is required for the efficient generation of Sc-K α radiation (4.093 keV).As a result, the peak of Sc-K α radiation (4.093 keV) is fairly weak, and the primary peak in the EDX spectrum of 5 keV is Sc-L α radiation (0.395 keV), which is indistinguishable from the N-K α radiation (0.392 keV) considering a spectral resolution of ~100 eV.The beam penetration depth within III-nitrides is approximately 200 nm for an accelerating voltage of 5 keV and 600 nm for 10 keV [28].At 10 keV, the intensity of Sc-K α radiation (4.093 keV) was enhanced by a factor of 2.5× that at 5 keV.Given the reduced electron beam interaction with the underlying AlN buffer layer, the intensity of Al-K α radiation (1.486 keV) at 5 keV is 6.4× that at 10 keV.Therefore, we chose an accelerating voltage of 5 keV for elemental mapping in order to maximize the contrast due to the inhomogeneous distribution of Al; meanwhile, we conducted EDX line scans at 5 keV to boost the intensity of Sc-K α radiation.We conducted EDX scans to investigate elemental distribution of Al and Sc across the films.EDX spectra taken under accelerating voltages of 5 keV and 10 keV were shown in Figure SM1 (Supplementary Material S1).The electron energy of 5 keV in the primary beam is slightly higher than the critical excitation energy of the K shell in Sc (4.492 keV).An overvoltage ratio of >2 is required for the efficient generation of Sc-Kα radiation (4.093 keV).As a result, the peak of Sc-Kα radiation (4.093 keV) is fairly weak, and the primary peak in the EDX spectrum of 5 keV is Sc-Lα radiation (0.395 keV), which is indistinguishable from the N-Kα radiation (0.392 keV) considering a spectral resolution of ~100 eV.The beam penetration depth within III-nitrides is approximately 200 nm for an accelerating voltage of 5 keV and 600 nm for 10 keV [28].At 10 keV, the intensity of Sc-Kα radiation (4.093 keV) was enhanced by a factor of 2.5× that at 5 keV.Given the reduced electron beam interaction with the underlying AlN buffer layer, the intensity of Al-Kα radiation (1.486 keV) at 5 keV is 6.4× that at 10 keV.Therefore, we chose an accelerating voltage of 5 keV for elemental mapping in order to maximize the contrast due to the inhomogeneous distribution of Al; meanwhile, we conducted EDX line scans at 5 keV to boost the intensity of Sc-Kα radiation.
EDX mappings in Figure 2 demonstrate that sample C2 grown at III/N = 0.78 has uniform Sc and Al distribution across the surface (see line scans in Figure SM2 of Supplementary Material), whereas the hillocks in sample C3 (III/N = 0.89) are characteristic of phase separation.Comparison between the SEM image in Figure 2d and the Al mapping in Figure 2f shows that the hillocks are Al-deficient microstructures with respect to the background.In Figure 2g, the EDX line scans further confirm that those Al-deficient hillocks have a higher Sc percentage compared to the surrounding regions.Considering the relatively low target Sc content x = 0.18, this type of phase separation could potentially be driven by surface kinetics [29].III/N atomic flux ratio governs adatom mobility, and an Nstable surface has a high energy barrier for Sc and Al adatom diffusion [30,31].We hypothesize that increasing III/N promotes higher Sc adatom mobility.The Sc adatoms, if  2d and the Al mapping in Figure 2f shows that the hillocks are Al-deficient microstructures with respect to the background.In Figure 2g, the EDX line scans further confirm that those Al-deficient hillocks have a higher Sc percentage compared to the surrounding regions.Considering the relatively low target Sc content x = 0.18, this type of phase separation could potentially be driven by surface kinetics [29].III/N atomic flux ratio governs adatom mobility, and an N-stable surface has a high energy barrier for Sc and Al adatom diffusion [30,31].We hypothesize that increasing III/N promotes higher Sc adatom mobility.The Sc adatoms, if not instantaneously incorporated into the metastable wurtzite lattice, could have a better chance to form the thermodynamically more-preferential rock-salt phase ScN, high-Sc-content Sc 1−y Al y N alloys, or intermetallic-phase Al 3 Sc during its diffusion at the growth front [23].Indeed, Figure S3 shows that the XRD (002) 2θ-ω scan of sample C3 exhibits a peak at ~38.0 • due to metallic cubic-phase Al 3 Sc [25], which is absent in the scan of sample C2.Both ScN and Al 3 Sc exhibit higher a Sc percentage compared to the target Sc content of x = 0.18; therefore, we observed high-Sc-content hillocks via EDX.

Characterization of Sc Composition and Crystal Quality of ScxAl1−xN Films
Structural characterization via XRD verified that the Sc composition of pure wurtzite ScxAl1−xN films grown on GaN/sapphire templates can be tuned from 0.16 to 0.37, and further increasing the Sc-to-Al atomic flux ratio leads to phase separation.In Figure 3b, the (002) 2θ-ω scan peaks of ScxAl1−xN are in the range of 35.9-36.5°,while the three peaks on the lower angle side are 34.5°from the GaN buffer layer, 35.7° from the sputtered 25 nm thick AlN nucleation layer with compressive strain, and 35.2° due to the satellite peak of AlN, respectively.For sample C9, the peak at 37.9° is likely from the metallic-phase Al3Sc [25].We observed slight variation in peak positions of samples C5-C9, indicating a lattice constant c in the range of 4.95-4.98Å.Our observation is consistent with the literature reports that c gradually increases by <1% with Sc composition from x = 0 to ~0.25 and then decreases [6,32,33].We conducted (102) 2θ-ω scans of ScxAl1−xN with skew angles of 42.6-40.8°.The structural deviation of ScxAl1−xN from GaN corresponds to a discrepancy of 0.6-2.4° in the angle between (002) and (102) planes, and as a result, no GaN (102) peak was observed in Figure 3c.The lattice constant a was derived and plotted with c in Figure 3d versus the Sc composition calculated assuming no residual strain in the ScxAl1−xN films.The Sc content of sample C9 is approximately the same as sample C8, even if the target Sc content based on the Sc-to-Al atomic flux design is higher at x = 0.44.Our observation of Sc composition saturation in the wurtzite phase, together with the emergence of the intermetallic-Al3Sc phase in the XRD (002) 2θ-ω scan [Figure 3b] and dual spots in RHEED patterns, indicates that the achievable Sc content for pure-wurtzite ScxAl1−xN by PA-MBE is x = 0.37 under a Tsub of 680 °C.We surveyed representative ScxAl1−xN samples via XPS, as shown in Figure 4, for sample C8.We analyzed the elemental composition after removing surface contaminants and oxides via an argon ion gun.The peaks with binding energies of 74.3 eV, 396.9 eV, 400.9 eV, and 405.3 eV correspond to Al 2p, N 1s, Sc 2p3/2, and Sc 2p1/2, respectively.The Sc content x of ScxAl1−xN was calculated from the peak areas of Sc 2p and Al 2p using the software Advantage (version 5.9931), which accounts for the sensitivity factors of each element.Subsequently, the ratio of the normalized peak areas of Sc 2p and Al 2p was used to determine the relative percentage of Sc in the ScxAl1−xN film, yielding a value of 38% for sample C8.The Sc composition derived from XRD is consistent with the XPS quantification within an error of ±1% (abs.). Figure 3e shows that the structural parameter c/a versus Sc composition decreases from 1.59 to 1.50 as x increases from 0.16 to 0.37, in comparison to the value of 1.60 for AlN.Although spontaneous polarization presents in an ideal wurtzite structure with c/a = 1.63 [34], structural nonideality, symbolized by a reduced c/a value, has a significant contribution to spontaneous polarization

Characterization of Sc Composition and Crystal Quality of Sc x Al 1−x N Films
Structural characterization via XRD verified that the Sc composition of pure wurtzite Sc x Al 1−x N films grown on GaN/sapphire templates can be tuned from 0.16 to 0.37, and further increasing the Sc-to-Al atomic flux ratio leads to phase separation.In Figure 3b, the (002) 2θ-ω scan peaks of Sc x Al 1−x N are in the range of 35.9-36.5 • , while the three peaks on the lower angle side are 34.5 • from the GaN buffer layer, 35.7 • from the sputtered 25 nm thick AlN nucleation layer with compressive strain, and 35.2 • due to the satellite peak of AlN, respectively.For sample C9, the peak at 37.9 • is likely from the metallic-phase Al 3 Sc [25].We observed slight variation in peak positions of samples C5-C9, indicating a lattice constant c in the range of 4.95-4.98Å.Our observation is consistent with the literature reports that c gradually increases by <1% with Sc composition from x = 0 to ~0.25 and then decreases [6,32,33].We conducted (102) 2θ-ω scans of Sc x Al 1−x N with skew angles of 42.6-40.8• .The structural deviation of Sc x Al 1−x N from GaN corresponds to a discrepancy of 0.6-2.4• in the angle between (002) and (102) planes, and as a result, no GaN (102) peak was observed in Figure 3c.The lattice constant a was derived and plotted with c in Figure 3d versus the Sc composition calculated assuming no residual strain in the Sc x Al 1−x N films.The Sc content of sample C9 is approximately the same as sample C8, even if the target Sc content based on the Sc-to-Al atomic flux design is higher at x = 0.44.Our observation of Sc composition saturation in the wurtzite phase, together with the emergence of the intermetallic-Al 3 Sc phase in the XRD (002) 2θ-ω scan [Figure 3b] and dual spots in RHEED patterns, indicates that the achievable Sc content for pure-wurtzite Sc x Al 1−x N by PA-MBE is x = 0.37 under a T sub of 680 • C. We surveyed representative Sc x Al 1−x N samples via XPS, as shown in Figure 4, for sample C8.We analyzed the elemental composition after removing surface contaminants and oxides via an argon ion gun.The peaks with binding energies of 74.3 eV, 396.9 eV, 400.9 eV, and 405.3 eV correspond to Al 2p, N 1s, Sc 2p 3/2 , and Sc 2p 1/2 , respectively.The Sc content x of Sc x Al 1−x N was calculated from the peak areas of Sc 2p and Al 2p using the software Advantage (version 5.9931), which accounts for the sensitivity factors of each element.Subsequently, the ratio of the normalized peak areas of Sc 2p and Al 2p was used to determine the relative percentage of Sc in the Sc x Al 1−x N film, yielding a value of 38% for sample C8.The Sc composition derived from XRD is consistent with the XPS quantification within an error of ±1% (abs.). Figure 3e shows that the structural parameter c/a versus Sc composition decreases from 1.59 to 1.50 as x increases from 0.16 to 0.37, in comparison to the value of 1.60 for AlN.Although spontaneous polarization presents in an ideal wurtzite structure with c/a = 1.63 [34], structural nonideality, symbolized by a reduced c/a value, has a significant contribution to spontaneous polarization [35].Therefore, the structural parameter reduction might have great potential for polarization engineering.[6,32,33].
Nanomaterials 2024, 14, x FOR PEER REVIEW 7 of 1 [35].Therefore, the structural parameter reduction might have great potential for polari zation engineering.Comparison of XRD ω rocking curve scans in Figure 3f,g reveals that the FWHMs of (002) scans have a marked degradation with increasing Sc composition, whereas the FWHMs of (102) scans are relatively constant in the range of 200-250 arcsec for various Sc compositions.At a low Sc content x < 0.20, the (002) FWHM of 450 arcsec increases by a factor of 3× with respect to that of the GaN.At x = 0.27, 0.37, and 0.39, (002) the FWHMs are 911 arcsec, 2156 arcsec, and 3524 arcsec, indicating a strong correlation between increasing screw/mixed dislocation density and decreasing lattice constant c.For reference, P. Wang et al. reported (002) FWHMs of 2200 arcsec for x = 0.30 and 2800 arcsec for x = 0.38 [11]; Hardy et al. reported XRD (002) FWHMs of 1840 arcsec for x = 0.32 [14] and 3190 arcsec for x = 0.39 [20].Comparison of ( 002) and (102) FWHMs of our samples with those high-Sc-content Sc x Al 1−x N epilayers in the literature can be found in Table S1 (Supplementary Material S3).Sc x Al 1−x N grown under even higher Sc-to-Al atomic flux ratios is characterized by 3D nucleation islands and lateral coalescence, which is evident by the spotty RHEED patterns in Figure 5d.The c-axis tilt of neighboring crystallites generates arrays of geometrically necessary screw/mixed threading dislocations at lowangle coincidence grain boundaries [36].The drastic increase in the (002) FWHM is a direct indicator of deteriorating random c-axis tilting, potentially due to inhomogeneous softening the wurtzite lattice with increasing Sc [37].Consequently, a reduction of piezoelectricity is expected with c-axis tilting [38,39].Surprisingly, negligible degradation has been observed in the (102) FWHMs, which implies superior epitaxial registry with the underlying GaN buffer layer.The ability to maintain in-plane crystalline orientation and to suppress fiber textures via MBE growth kinetics in comparison to physical sputtering techniques could be a distinctive advantage in device operation that relies on in-plane properties such as d 31 [40].Comparison of XRD ω rocking curve scans in Figure 3f,g reveals that the FWHMs of (002) scans have a marked degradation with increasing Sc composition, whereas the FWHMs of (102) scans are relatively constant in the range of 200-250 arcsec for various Sc compositions.At a low Sc content x < 0.20, the (002) FWHM of 450 arcsec increases by a factor of 3× with respect to that of the GaN.At x = 0.27, 0.37, and 0.39, (002) the FWHMs are 911 arcsec, 2156 arcsec, and 3524 arcsec, indicating a strong correlation between increasing screw/mixed dislocation density and decreasing lattice constant c.For reference, P. Wang et al. reported (002) FWHMs of 2200 arcsec for x = 0.30 and 2800 arcsec for x = 0.38 [11]; Hardy et al. reported XRD (002) FWHMs of 1840 arcsec for x = 0.32 [14] and 3190 arcsec for x = 0.39 [20].Comparison of (002) and (102) FWHMs of our samples with those

High Sc-Content Sc x Al 1−x N Films and Phase Separation
Figure 5 demonstrates the evolution of the RHEED patterns and surface morphology of Sc x Al 1−x N films grown on GaN/sapphire templates with the increasing Sc-to-Al atomic flux ratio.We observed spotty-modulated-streaky RHEED patterns with faint high-order 2× streaks (indicated by red arrows) for x = 0.18-0.37(samples C6-C9), signifying the presence of surface-reconstruction during growth.No ring-like features were present in the RHEED patterns, consistent with the low XRD (102) ω rocking curve FWHMs in Figure 3h.Samples C6-C8 exhibit a relatively smooth surface, and the increase in Sc content has a subtle effect on the surface microstructure.For x = 0.18 (sample C6), the surface has a granular structure decorated with pits and hillocks of 30-70 nm in diameter [Figure 5a].A pit density of the order of 10 8 cm −2 was also observed from the GaN buffer layer, potentially related to impurities on the substrate surface [41] or screw/mixed dislocations.In Figure 5a, the density of pits approximates 1.4 × 10 9 cm −2 , higher than the screw/mixed dislocation density of 4.5 × 10 8 cm −2 derived from XRD ω rocking curve FWHMs.As the Sc percentage increases, the surface changes from granular to atomic step flows (sample C8) with a reduction in the pit density to 2.0 × 10 8 cm −2 .However, at higher Sc-to-Al atomic flux ratios of 80%, the RHEED patterns become spotty, with giant hillocks of 300-400 nm in diameter formed on the surface.In Figure 5d, dual spots on both sides of the primary streaks indicate reflections from the (111) and (002) planes of rock-salt-phase Sc x Al 1−x N [20,42].EDX mappings in Figure 6a-c  A pit density of the order of 10 8 cm −2 was also observed from the GaN buffer layer, potentially related to impurities on the substrate surface [41] or screw/mixed dislocations.In Figure 5a, the density of pits approximates 1.4 × 10 9 cm −2 , higher than the screw/mixed dislocation density of 4.5 × 10 8 cm −2 derived from XRD ω rocking curve FWHMs.As the Sc percentage increases, the surface changes from granular to atomic step flows (sample C8) with a reduction in the pit density to 2.0 × 10 8 cm −2 .However, at higher Sc-to-Al atomic flux ratios of 80%, the RHEED patterns become spotty, with giant hillocks of 300-400 nm in diameter formed on the surface.In Figure 5d, dual spots on both sides of the primary streaks indicate reflections from the (111) and (002) planes of rock-salt-phase ScxAl1−xN [20,42].EDX mappings in Figure 6a-c   In literature, a transition regime of mixed ScxAl1−xN phases was universally observed.S. satoh et al. reported the transition from the wurtzite phase to the wurtzite-rock salt twophase mixture at x = 0.30-0.35,and from the two-phase mixture to the rock salt phase at x = 0.38-0.43[43].Hoglund et al. reported that phase transition from a mixture of two phases of rock salt and wurtzite to a pure-rock-salt phase occurs at x = 0.40-0.48,depending on the seed layer [21,22].In addition, Hoglund et al. reported phase separation of ScxAl1−xN for x > 0.23 with the emergence of a rock salt ScN(111) peak in (002) 2θ-ω scans [21].Herein, we identified the boundary of the stable wurtzite phase at x = 0.37-0.39,and in proximity to the boundary, we attained pure-wurtzite-phase smooth Sc0.37Al0.63Nthin films based on XRD, RHEED, and EDX analysis.The piezoelectric response of the Sc0.37Al0.63Nthin film (sample C8) was confirmed via PFM experiments.The surface morphology, out-of-plane piezoelectric amplitude, and phase diagrams in Figure 7 confirm that an external electric field of 1.5 MV/cm has selectively flipped the polarity by 180° with In literature, a transition regime of mixed Sc x Al 1−x N phases was universally observed.S. satoh et al. reported the transition from the wurtzite phase to the wurtzite-rock salt two-phase mixture at x = 0.30-0.35,and from the two-phase mixture to the rock salt phase at x = 0.38-0.43[43].Hoglund et al. reported that phase transition from a mixture of two phases of rock salt and wurtzite to a pure-rock-salt phase occurs at x = 0.40-0.48,depending on the seed layer [21,22].In addition, Hoglund et al. reported phase separation of Sc x Al 1−x N for x > 0.23 with the emergence of a rock salt ScN(111) peak in (002) 2θ-ω scans [21].Herein, we identified the boundary of the stable wurtzite phase at x = 0.37-0.39,and in proximity to the boundary, we attained pure-wurtzite-phase smooth Sc 0.37 Al 0.63 N thin films based on XRD, RHEED, and EDX analysis.The piezoelectric response of the Sc 0.37 Al 0.63 N thin film (sample C8) was confirmed via PFM experiments.The surface morphology, out-of-plane piezoelectric amplitude, and phase diagrams in Figure 7 confirm that an external electric field of 1.5 MV/cm has selectively flipped the polarity by 180 • with clear antiparallel domain boundaries.The piezoelectric amplitude at domain boundaries is at least one order of magnitude lower than that within each domain, which is a representative aspect of ferroelectricity due to the cancellation of polarization from opposite domains on either side.clear antiparallel domain boundaries.The piezoelectric amplitude at domain boundaries is at least one order of magnitude lower than that within each domain, which is a representative aspect of ferroelectricity due to the cancellation of polarization from opposite domains on either side.Two different types of phase separation with degraded surface morphology have been identified in ScxAl1−xN films grown under N-rich conditions.For the first scenario, a relatively high III/N atomic flux ratio of 0.89 with a fixed Sc-to-Al flux ratio causes Scagglomerated hillocks, whereas the target Sc content of x = 0.18 is much lower compared to the generally reported phase transition boundary of x ~ 0.30-0.43[43].Cubic-phase intermetallic Al3Sc was identified in sample C3 via XRD, which has higher Sc compared to the target Sc content of x = 0.18 in the wurtzite phase, and this is consistent with the observation of high-Sc-content, Al-deficient hillocks.Therefore, a sufficiently high over-flux of active N is mandatory to suppress Sc adatom migration and to facilitate the homogeneous incorporation of Sc into the wurtzite lattice.Boosting Sc adatom mobility with an increased III/N ratio, however, could drive the nucleation of thermodynamically preferential cubic-phase intermetallic Al3Sc and the rock salt phase of ScN, leading to high-Sccontent hillocks.For the second scenario with a fixed III/N ratio of 0.78, a high Sc-to-Al atomic flux ratio of 80% causes high-Sc-content rock-salt-phase ScxAl1−xN, as evidenced by RHEED and intermetallic Al3Sc hillocks identified via XRD, which has a significantly higher Al percentage compared to the measured Al content of (1 − x) = 0.61 in the wurtzite phase.The high-Al-content, Sc-deficient hillocks observed via EDX indicates that the primary elemental inhomogeneity originates from Al3Sc, whereas the high-Sc-content rocksalt-phase ScxAl1−xN could be uniformly embedded into the primary wurtzite phase thin film.The non-linear composition dependence of the bond angle and bond length at the phase transition boundary causes structural instability of the ScxAl1−xN wurtzite lattice [37], which explains why the wurtzite lattice is "saturated" with the incorporation of 39% percent of Sc.Excessive Sc adatoms drive the formation of thermodynamically stable rock salt ScN and metallic Al3Sc.Therefore, the surface kinetics of Sc adatoms plays a critical role in the phase degradation of ScxAl1−xN.

Conclusions
Wurtzite-phase ScxAl1−xN (0.16 ≤ x ≤ 0.37) thin films were grown by precisely tuning the atomic fluxes of Sc, Al, and active N species.We identified two types of phase separation closely related to MBE growth kinetics.At the optimal III/N ratio of 0.78, increasing the Sc-to-Al flux ratio to >60% led to cubic-phase intermetallic Al3Sc and high-Sc-content rock-salt-phase ScxAl1−xN, indicating a phase transition boundary at x = 0.37-0.39.EDX mappings proved the presence of high-Al-content hillocks across the sample surface.We hypothesized that structural instability of ScxAl1−xN at the phase transition boundary pro- Two different types of phase separation with degraded surface morphology have been identified in Sc x Al 1−x N films grown under N-rich conditions.For the first scenario, a relatively high III/N atomic flux ratio of 0.89 with a fixed Sc-to-Al flux ratio causes Sc-agglomerated hillocks, whereas the target Sc content of x = 0.18 is much lower compared to the generally reported phase transition boundary of x ~0.30-0.43[43].Cubic-phase intermetallic Al 3 Sc was identified in sample C3 via XRD, which has higher Sc compared to the target Sc content of x = 0.18 in the wurtzite phase, and this is consistent with the observation of high-Sc-content, Al-deficient hillocks.Therefore, a sufficiently high over-flux of active N is mandatory to suppress Sc adatom migration and to facilitate the homogeneous incorporation of Sc into the wurtzite lattice.Boosting Sc adatom mobility with an increased III/N ratio, however, could drive the nucleation of thermodynamically preferential cubic-phase intermetallic Al 3 Sc and the rock salt phase of ScN, leading to high-Sc-content hillocks.For the second scenario with a fixed III/N ratio of 0.78, a high Sc-to-Al atomic flux ratio of 80% causes high-Sc-content rock-salt-phase Sc x Al 1−x N, as evidenced by RHEED and intermetallic Al 3 Sc hillocks identified via XRD, which has a significantly higher Al percentage compared to the measured Al content of (1 − x) = 0.61 in the wurtzite phase.The high-Al-content, Sc-deficient hillocks observed via EDX indicates that the primary elemental inhomogeneity originates from Al 3 Sc, whereas the high-Sccontent rock-salt-phase Sc x Al 1−x N could be uniformly embedded into the primary wurtzite phase thin film.The non-linear composition dependence of the bond angle and bond length at the phase transition boundary causes structural instability of the Sc x Al 1−x N wurtzite lattice [37], which explains why the wurtzite lattice is "saturated" with the incorporation of 39% percent of Sc.Excessive Sc adatoms drive the formation of thermodynamically stable rock salt ScN and metallic Al 3 Sc.Therefore, the surface kinetics of Sc adatoms plays a critical role in the phase degradation of Sc x Al 1−x N.

Conclusions
Wurtzite-phase Sc x Al 1−x N (0.16 ≤ x ≤ 0.37) thin films were grown by precisely tuning the atomic fluxes of Sc, Al, and active N species.We identified two types of phase separation closely related to MBE growth kinetics.At the optimal III/N ratio of 0.78, increasing the Sc-to-Al flux ratio to >60% led to cubic-phase intermetallic Al 3 Sc and high-Sc-content rock-salt-phase Sc x Al 1−x N, indicating a phase transition boundary at x = 0.37-0.39.EDX

Figure 1 .
Figure 1.Reflection high-energy electron diffraction (RHEED) and planar-view scanning electron microscope (SEM) images of Sc 0.18 Al 0.82 N films (samples C1-C4) grown on Si (111) substrates with different III/N atomic flux ratios.RHEED patterns of Sc 0.18 Al 0.82 N epilayers along [1120] and [1100] during growth are shown.The III/N ratios are (a) 0.69 for sample C1, (b) 0.78 for sample C2, (c) 0.89 for sample C3, and (d) 1.12 for sample C4.EDX mappings in Figure 2 demonstrate that sample C2 grown at III/N = 0.78 has uniform Sc and Al distribution across the surface (see line scans in Figure S2 of Supplementary Materials), whereas the hillocks in sample C3 (III/N = 0.89) are characteristic of phase separation.Comparison between the SEM image in Figure2dand the Al mapping in Figure2fshows that the hillocks are Al-deficient microstructures with respect to the background.In Figure2g, the EDX line scans further confirm that those Al-deficient hillocks have a higher Sc percentage compared to the surrounding regions.Considering the relatively low target Sc content x = 0.18, this type of phase separation could potentially be driven by surface kinetics[29].III/N atomic flux ratio governs adatom mobility, and an N-stable surface has a high energy barrier for Sc and Al adatom diffusion[30,31].We hypothesize that increasing III/N promotes higher Sc adatom mobility.The Sc adatoms, if not instantaneously incorporated into the metastable wurtzite lattice, could have a better chance to form the thermodynamically more-preferential rock-salt phase ScN, high-Sc-content Sc 1−y Al y N alloys, or intermetallic-phase Al 3 Sc during its diffusion at the growth front[23].Indeed, FigureS3shows that the XRD (002) 2θ-ω scan of sample C3 exhibits a peak at ~38.0 • due to metallic cubic-phase Al 3 Sc[25], which is absent in the scan of sample C2.Both ScN and Al 3 Sc exhibit higher a Sc percentage compared to the target Sc content of x = 0.18; therefore, we observed high-Sc-content hillocks via EDX.

Figure 2 .
Figure 2. Energy-dispersive X-ray (EDX) spectroscopy analysis of sample C2 (III/N = 0.78) and sample C3 (III/N = 0.89): (a) SEM, (b) Sc, and (c) Al mappings of sample C2; (d) SEM, (e) Sc, and (f) Al mappings of sample C3; (g) EDX line scan of sample C3 along the dashed red line showing that the hillocks have higher Sc and lower Al percentages with respect to the background.The electron beam energy is 10 keV for all EDX mappings and the line scan of Al (green).The beam energy is 5 keV for the line scan of Sc (cyan) in (g).

Figure 2 .
Figure 2. Energy-dispersive X-ray (EDX) spectroscopy analysis of sample C2 (III/N = 0.78) and sample C3 (III/N = 0.89): (a) SEM, (b) Sc, and (c) Al mappings of sample C2; (d) SEM, (e) Sc, and (f) Al mappings of sample C3; (g) EDX line scan of sample C3 along the dashed red line showing that the hillocks have higher Sc and lower Al percentages with respect to the background.The electron beam energy is 10 keV for all EDX mappings and the line scan of Al (green).The beam energy is 5 keV for the line scan of Sc (cyan) in (g).

Figure 3 .
Figure 3. Structural characterization of ScxAl1−xN thin films (samples C5-C9) grown on GaN/sapphire templates via X-ray diffraction (XRD): (a) structural schematics of the samples; (b) (002) and (c) (102) 2θ-ω scans of the samples (the (002) 2θ-ω scan of the GaN/sapphire template is included in (b) to show the peaks of GaN and AlN); (d) lattice constant a and c versus Sc content in wurtzite ScxAl1−xN calculated assuming no residual strain; (e) calculated structural parameter c/a versus Sc content; (f) (002) and (g) (102) ω rocking curve scans of the samples; (h) full width at half-maximum (FWHM) of the ω rocking curves in (f,g).The calculated Sc content is used to label each sample in other images.The shadows in (d,e) indicate the ranges of the lattice parameters or structural parameters reported in the literature [6,32,33].

Figure 3 .
Figure 3. Structural characterization of Sc x Al 1−x N thin films (samples C5-C9) grown on GaN/ sapphire templates via X-ray diffraction (XRD): (a) structural schematics of the samples; (b) (002) and (c) (102) 2θ-ω scans of the samples (the (002) 2θ-ω scan of the GaN/sapphire template is included in (b) to show the peaks of GaN and AlN); (d) lattice constant a and c versus Sc content in wurtzite Sc x Al 1−x N calculated assuming no residual strain; (e) calculated structural parameter c/a versus Sc content; (f) (002) and (g) (102) ω rocking curve scans of the samples; (h) full width at half-maximum (FWHM) of the ω rocking curves in (f,g).The calculated Sc content is used to label each sample in other images.The shadows in (d,e) indicate the ranges of the lattice parameters or structural parameters reported in the literature [6,32,33].

Figure 3 .
Figure 3. Structural characterization of ScxAl1−xN thin films (samples C5-C9) grown on GaN/sap phire templates via X-ray diffraction (XRD): (a) structural schematics of the samples; (b) (002) and (c) (102) 2θ-ω scans of the samples (the (002) 2θ-ω scan of the GaN/sapphire template is included in (b) to show the peaks of GaN and AlN); (d) lattice constant a and c versus Sc content in wurtzit ScxAl1−xN calculated assuming no residual strain; (e) calculated structural parameter c/a versus S content; (f) (002) and (g) (102) ω rocking curve scans of the samples; (h) full width at half-maximum (FWHM) of the ω rocking curves in (f,g).The calculated Sc content is used to label each sample in other images.The shadows in (d,e) indicate the ranges of the lattice parameters or structural param eters reported in the literature [6,32,33].
validate the homogeneous distribution of Sc and Al in sample C8. Figure 6d-g reveal that hillocks in samples C9 are Al-agglomerated, Sc-deficient microstructures, which potentially correspond to the metallic Al 3 Sc droplets observed via XRD (002) 2θ-ω scan [Figure 3b].The dual spots of rock salt Sc x Al 1−x N in RHEED [Figure 5d] are likely high-Sc-content alloys with XRD (002) 2θ-ω scan peak at ~34.5 • obscured by the GaN peak [42].Negligible desorption of Sc and Al adatoms is expected at T sub = 680 • C. While the Sc composition in the wurtzite phase is almost identical for samples C8 and C9, a further increase in the Sc-to-Al atomic flux ratio from 60% (sample C8) to 80% (sample C9) led to Sc-deficient metallic Al 3 Sc and high-Sc-content rock salt Sc x Al 1−x N. Nanomaterials 2024, 14, x FOR PEER REVIEW 9 of 13RHEED patterns, consistent with the low XRD (102) ω rocking curve FWHMs in Figure3h.Samples C6-C8 exhibit a relatively smooth surface, and the increase in Sc content has a subtle effect on the surface microstructure.For x = 0.18 (sample C6), the surface has a granular structure decorated with pits and hillocks of 30-70 nm in diameter [Figure5a].
validate the homogeneous distribution of Sc and Al in sample C8. Figure 6d-g reveal that hillocks in samples C9 are Al-agglomerated, Scdeficient microstructures, which potentially correspond to the metallic Al3Sc droplets observed via XRD (002) 2θ-ω scan [Figure 3b].The dual spots of rock salt ScxAl1−xN in RHEED [Figure 5d] are likely high-Sc-content alloys with XRD (002) 2θ-ω scan peak at ~34.5°obscured by the GaN peak [42].Negligible desorption of Sc and Al adatoms is expected at Tsub = 680 °C.While the Sc composition in the wurtzite phase is almost identical for samples C8 and C9, a further increase in the Sc-to-Al atomic flux ratio from 60% (sample C8) to 80% (sample C9) led to Sc-deficient metallic Al3Sc and high-Sc-content rock salt ScxAl1−xN.

Figure 6 .
Figure 6.EDX spectroscopy analysis of sample C8 and sample C9: (a) SEM, (b) Sc, and (c) Al mappings of sample C8; (d) SEM, (e) Sc, and (f) Al mappings of sample C9; (g) EDX line scan of sample C9 along the dashed red line showing that the hillocks have lower Sc and higher Al percentages with respect to the background.The electron beam energy is 10 keV for all EDX mappings and the line scan of Al (green).The beam energy is 5 keV for the line scan of Sc (cyan) in (g).

Figure 6 .
Figure 6.EDX spectroscopy analysis of sample C8 and sample C9: (a) SEM, (b) Sc, and (c) Al mappings of sample C8; (d) SEM, (e) Sc, and (f) Al mappings of sample C9; (g) EDX line scan of sample C9 along the dashed red line showing that the hillocks have lower Sc and higher Al percentages with respect to the background.The electron beam energy is 10 keV for all EDX mappings and the line scan of Al (green).The beam energy is 5 keV for the line scan of Sc (cyan) in (g).

Figure 7 .
Figure 7. Piezoelectric force microscopy (PFM) analysis of the Sc0.37Al0.63Nthin film grown on GaN/sapphire (samples C8): (a) surface morphology; (b) out-of-plane piezoelectric amplitude; and (c) phase diagrams under an external voltage of ±15 V versus the GaN buffer layer.The scan area is 40 µm × 40 µm, and the RMS is 4.41 nm.

Figure 7 .
Figure 7. Piezoelectric force microscopy (PFM) analysis of the Sc 0.37 Al 0.63 N thin film grown on GaN/sapphire (samples C8): (a) surface morphology; (b) out-of-plane piezoelectric amplitude; and (c) phase diagrams under an external voltage of ±15 V versus the GaN buffer layer.The scan area is 40 µm × 40 µm, and the RMS is 4.41 nm.